Problem: Divide. Write your answer in simplest form. $ -\dfrac{4}{5} \div \left(-\dfrac{7}{6}\right) = {?} $
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $-\dfrac{7}{6}$ is $-\dfrac{6}{7}$. Therefore: $ -\dfrac{4}{5} \div \left(-\dfrac{7}{6}\right) = -\dfrac{4}{5} \times \left(-\dfrac{6}{7}\right) $ $ \phantom{-\dfrac{4}{5} \div \left(-\dfrac{7}{6}\right)} = \dfrac{-4 \times (-6)}{5 \times 7} $ $ \phantom{-\dfrac{4}{5} \div \left(-\dfrac{7}{6}\right)} = \dfrac{24}{35} $